Solve sqrt{62*1/2/7}

$$\sqrt { \frac { 62 \times \frac { 1 } { 2 } } { 7 } }$$

Evaluate

$$\frac{\sqrt{217}}{7}\approx 2.104417123$$

Solution Steps

Multiply 62 and \frac{1}{2} to get \frac{62}{2}.

$$\sqrt{\frac{\frac{62}{2}}{7}}$$

Divide 62 by 2 to get 31.

$$\sqrt{\frac{31}{7}}$$

Rewrite the square root of the division \sqrt{\frac{31}{7}} as the division of square roots \frac{\sqrt{31}}{\sqrt{7}}.

$$\frac{\sqrt{31}}{\sqrt{7}}$$

Rationalize the denominator of \frac{\sqrt{31}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{31}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{31}\sqrt{7}}{7}$$

To multiply \sqrt{31} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{217}}{7}$$